We report a molecular dynamics study of the structure and dynamics of water at a clay surface. The negative charge of the surface and the presence of surface oxygen atoms perturbs water over two to three molecular layers, while the nature of the counterions (Na(+)or Cs(+)) has only a small effect. In the first molecular layer, approximately half of the water molecules are H-bonded to the surface. We also analyze the H-bond network between surface water molecules. The diffusion of water molecules along the surface is slowed down compared to the bulk case. As far as the orientational order and dynamics of the water dipole are concerned, only the component normal to the clay surface is perturbed. We investigate the surface H-bond formation and dissociation dynamics and their coupling to the release of molecules from the first molecular layer. We introduce a simple kinetic model in the spirit of Luzar and Chandler [Nature, 1996, 379, 55] to allow for a comparison with bulk water dynamics. This model semi-quantitatively reproduces the molecular simulation results and suggests that H-bond formation is faster with the surface than in the bulk, while H-bond dissociation is slower.